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Financial Appraisal in Project Financial Appraisal in Project Scanning and SelectionScanning and Selection

TIME VALUE OF MONEY

Money value can be increased if it keeps on rolling.

This is what is known as time value of money.

Year 0 1 2 3 4

Rs. -1,000

250 250 250 250

Compounding:

The future value of money that is available today can be calculated using the concept of Compounding and that value is known as Future Value ( FV) or Compounded Value ( CV).

Discounting:The present value of money accruing later is estimated by the process of Discounting and the value is known as Present Value ( PV) or Discounted Value (DV).

Understanding Time Value of Money

Cash outflow in the beginning

(year 0)

Cash inflow in year 1




-1000 250 250 250 250

+FV(250)

+FV(250)

+FV(250)

+FV(-1000)

Table 1 – Process of Compounding

Cash outflow in the beginning

(year 0)





-1000 250 250 250 250

+PV(250)

+PV(250)

+PV(250)

+PV(250)

Table 2: Process of Discounting

Simple Interest: The future value (FV) of a sum of money invested at a given annual rate of interest will depend on whether the interest is paid only on the original investment ( called Simple Interest). Compound Interest: It is calculated on the original investment plus accrued interest ( called Compound Interest). In the case of compound interest, there is a further factor affecting the future value, namely the frequency with which interest is paid (e.g. monthly, quarterly or annually).

With simple interest, the future value is determined by:FVn = V0(1+i*n),

where , FVn = future value at time n,

V0 = original sum invested or the principal value

i = annual rate of simple interest

Say, you win Rs.100,000 from a TV Realty Show and decide to invest in Fixed deposit of a commercial bank at a simple interest of 10% for five years. The future value will be the original of Rs.100000 plus five years interest, giving a total of Rs.150,000.FV5 = Rs.100,000 [1+ (0.10)(5)] = Rs.150,000.

Compounded or Future Value

If i is compound interest, in subsequent years the interest is paid on the original capital plus accrued interest. FV(i,n) = V0(1+i)n

Suppose your Rs.100000 investment was put into a building society paying a fixed 10% compound interest yearly. What will your investment be worth after five years? In one year time, the investment will be worth

100,000(1+0.10) = Rs.110,000After 2 years it will be worth 100,000(1+0.10)2 = 121,000After 5 years it will be worth: FV5 = 100,000(1+0.10)5 = 161,000

Hence the effect of compound interest yields a much higher value than simple interest, which yielded 150000.


The generalized formula for these shorter compounding period is FVn = V0( 1+

k/m)m*n, where m is no. of years compounding is done & k is nominal interest rate.

Suppose you deposit Rs.20,000 with an investment company which pays 12% interest with quarterly compounding. How much will this deposit grow in 5 years?Solution :FV = 20,000 * (1+0.12/4)4*5 = 20,000(1+.03)20 =Rs.36,120

More Frequent Compounding

Annual Percentage Rate (APR) for a Loan:

Annually (1+0.22) -1 0.22 or 22%

Semi-annually (1+0.22/2)2 – 1 0.232 or 23.2%Quarterly (1+0.22/4)4 – 1 0.239 or 23.9%Monthly (1+0.22/12)12 – 1 0.244 or 24.4%Daily (1+0.22/365)365 – 1 0.246 or 24.6%


Effective interest rate= r = (1+k/m)m -1,

Where r = effective interest rate, k = nominal interest rate, m = frequency of compounding per year

If the nominal interest rate is 10% and frequency of compounding is half yearly, the effective interest rate is

r = (1+k/m)m -1 = ( 1+ .10/2)2 – 1 = .1025 or 10.25%


A frequent question asked by the investor is, “ How long it will take to make an amount double for a certain rate of interest?”

This question can be answered by a thumb rule known as ‘rule of 72’ or ‘rule of 69’.

By rule of 72 , DP = 72/i for an interest rate = i%.

By rule of 69, DP = 0.35 + 69/i for an interest rate = i%.

Example :

Find out the doubling period for an interest rate of 10% by applying the two rules.

By rule of 72 , DP = 72/i for an interest rate of i% = 72/10 = 7.2 years.

By rule of 69, DP = 0.35 + 69/i for an interest rate of i% = 0.35 + 69/10 = 0.35 + 6.9 = 7.25 years.

Doubling Period (DP)

Future Value

An alternative way of assessing the worth of an investment is to invert the compounding process to give the present value of the future cash flows. This process is called discounting. Today’s value of any future cash flow is known as Discounted or Present Value.

.

Discounting is the process of adjusting future cash flows to their present values. It is, in effect, compounding in reverse.

Discounted or Present Value

n

We have seen that Future Value

Dividing both sides by (1+i)n,

Example :Compute the present value of Rs.1,611 receivable after 5 years at the rate of 10% .

Note: Do not pay more than Rs.1,000 today for an investment offering a certain return of Rs.1,611 after 5 years, assuming a 10% market rate of interest.

Future Value

It is useful to see how the discounting process affects present values at different rates of interest. This is seen in the following figure that the value of Rs.1 decreases as the rate and period increases from 0 to 20% and within 0 - 25 years.

year 10% 15% 20%0 1.0 1.0 1.05 0.6 0.5 0.4

10 0.4 0.25 0.1615 0.24 0.12 0.0620 0.15 0.06 0.0325 0.19 0.03 0.01

Present value of a single future sum Rs.1

Effect of discounting

Present value(Rs) %

1.0

0.75 5%

0.5 10%

0.25 15%

0.0 20%

Period(years) 2 4 6 8 10

Discount factors

The relationship between present value of Rs.1 and interest over time

Much of the medium of using formulae and power functions can be eased by using discount tables or computer based spreadsheet packages. The discount factor or interest factor Rs.1 for a 10% discount rate in three years’ time is:

1/(1.10)3= 1/1.33 = 0.751

PVIF(i, n)= 1/(1+i)n

Present value formula

The inverse of PVIF is Future Value Interest Factor (FVIF). The above equation can be written as follows:

PVn = Present Value = FVn = FVn * PVIF(i,n)

(1+i)n

Therefore, Compounded value or Future value = FVn = PVn* (1+i)n = PVn* FVIF(i,n).

FVIF(i,n) = (1+i)n

Therefore, PVIF(i,n) = 1/ FVIF(i,n)

Future value formula

Rama Raju promises you to give you Rs.5,000 after 10 years in exchange for Rs.1,000 today. What interest is implicit in his offer?

Let i be the rate of interest.

It is given that Rs.1000* FVIF(i,10) = 5000, FVIF(i,10) = 5

From the tables we find FVIF(16,10) = 4.411

And FVIF(18,10)= 5.234

Applying a linear approximation in the interval, we get

i = 16% + 2% * (5.0—4.4111) = 17.4%. (5.234—4.411)

Example

Present Value

An annuity is an investment paying a fixed sum each year(A) for a specified period of time(n) at the rate of interest k. Examples of annuities include many credit agreements and house mortgages.

Present Value of an annuityThe present value of a regular annuity can be represented in terms of the symbols defined in the table as follows:

PVAn = A/(1+i) + A/(1+i)2 + A/(1+i)3+ -------------+A/(1+i)n ------- (1)

Multiplying both sides by (1+i) we get,

PVAn(1+i) = A + A/(1+i) + A/(1+i)2+ ----------+A(1+i)n-1 ------------(2)

Subtracting equation (1) from equation (2), we get

PVAni = A – A/(1+i)n = A[ 1 – 1/(1+i)n]

PVAn = A [(1+i)n – 1] = A*PVIFA(i,n)

i* (1+i)n

Annuity

Time Amount Amount Amount Amount Amount

1

2

3

4

5

PV

1,000

1,000

1,000

+1,000(1.1)-1

1,000

+1,000(1.1)-2

1,000

+1,000(1.1)-3

1,000

+1,000(1.1)-4

Example :Suppose an annuity of Rs.1000 is issued for 20 years at 10%. Using the table Z1 in Appendix 2, we can find the present value as follows:PVA(10,20) = Rs.1,000 * PVIFA(10,20) = Rs.1,000 * 8.5136 = Rs.8,513.60

Present Value Of Annuity

The future value of a regular annuity can be expressed as follows:FVAn = A(1+i)n-1 +A(1+i)n-2 + ----- A ------------------------------------------------(3)

Multiplying equation (3) by (1+i) on both sides, we getFVAn(1+i) = A(1+i)n +A(1+i)n-1 + ----- A(1+i) --------------------------------------(4)

Subtracting equation (3) from equation (4), we getFVAn = A[(1+i)n – 1]/i = A* FVIFA(i,n)

Therefore, PVIFA(i,n) = FVIFA(i,n)*PVIF(i,n)

Future value of an annuity

Example :You can save Rs.6,000 a year for 5 years. What will be these savings cumulate to at the end of 10 years, if the rate of interest is 10%?The accumulated value after 10 years will be as follows:

= Rs.[6,000*FVIFA(10,5)*FVIF(10,5)] = Rs.[6000*6.105*1.611] = Rs.59010.93

Time Amount Amount Amount Amount Amount1

2

3

4

5

FV

1,000

1,000(1.1)5

1,000

+1,000(1.1)4

1,000

+1,000(1.1)3

1,000

+1,000(1.1)2

1,000

+1,000(1.1)

Future value of an annuity

In case of annuity, it is generally assumed that payment has been made at the end of each year. If the payment is made at the beginning of each year, then this is called annuity due and it’s value is found by the product of the value (either present or future) of a regular annuity and the factor (1+i).

FVAn(due) = A*FVIFA(i,n)*(1+i)

PVAn(due) = A*PVIFA(i,n)*(1+i)

Example :

What is the present value of a 5 year annuity due of Rs. 5,000 at 10%?

PVAn(due) = A*PVIFA(i,n)*(1+i) = Rs.5,000*PVIFA(10,5)*(1+0.1) = Rs.2,0850.50

PerpetuityFrequently, an investment pays a fixed sum each year for a specified number of years. A series of annual receipts or payments is termed an annuity. The simplest form of an annuity for an infinite series is called Perpetuity.

Annuity Due

PVperpetuity = A/i

Example :Uncle Shyam wishes to leave you in his will an annual sum of Rs.10,000 a year starting next year. Assuming an interest rate of 10%, how much of his estate must be set aside for this purpose?

PVperpetuity = A/iPV = Rs.10,000/0.1 = Rs.100,000

Let your benevolent uncle now wishes to compensate for inflation estimated to be at 6% per annum (say).

Then PV = A/(i-g) = Rs.10,000/(0.1-0.06) = 250,000.Similarly, Present value of growing perpetuity = A/ (i-g) where, g = growth rate.

Perpetuity

We know that PV = FV* PVIF(i,n)

Therefore, PVIF(i,n) = PV/FV = 1/(1+i)n

Or, (1+i)n = FV/PV

i = (FV/PV)1/n - 1

Example :

A credit company may offer to lend you Rs.1,000 today on condition that you repay Rs. 1,643 at the end of three years. Then what is the compound interest rate for this offer?

i = (1643/1000)1/3 – 1 = 18%

Calculating interest rates

Cost of Capital

The cost of source of finance is defined as the rate of discount which equates the present value of the expected payments to that source of finance with the net proceeds received from the same source.

Opportunity Cost of Capital

The first step in calculating a company’s Weighted Average Cost of Capital (WACC) is to calculate the cost of the individual components of its capital. Here we consider the different sources of long-term finance available to a company and how to calculate the cost of using the source.

Discounted Cash Flow (DCF) Approach:

According to the Dividend Forecast Approach, the intrinsic value of an equity stock is equal to the sum of the present values of the dividends associated with it, i.e.,Pe = ∑ Dt / (1+ke)

t for t= 1 to n

Where, Pe = price per equity share, Dt = expected dividend per share at the end of year t,

And ke = rate of return required by the equity shareholders.

Pe = D1 / (ke – g)

Or, ke = (D1/Pe ) + g = {D0(1+g)/P0} + g

where P0 = ex-dividend current share price, g = expected annual increase in dividends, D0 = dividend

to be paid shortly, D1 = dividend to be paid after one year.

Cost of Equity – DCF Approach

Using the CAPM, the cost of equity finance is given by the following linear relationship:

kj = Rf + βj*(Rm – Rf)

Where, kj = the rate of return of security j predicted by the model

Rf = the risk-free rate of return

βj = the beta coefficient of security j

Rm = the return of the market

Capital Asset Pricing Model (CAPM)

kx = Bond yield + risk premium = 9% +4% =13%.

Bond-Yield-Plus-Risk-Premium-Approach

The cost of retained earnings or internal accruals is generally taken to be the same as the cost of equity, i.e. , kr representing cost of retained earnings) = ke.

But when for raising external equity, the company has to incur certain floatation costs (cost incurred during public issue, like brokerage, underwriting commission, fees to managers of issue, legal charges, advertisement and printing expenses etc.). The formula for ke in this

case will be as follows:

ke = kr / (1-f) where, f = floatation costs.

Example :Gorky Ltd. has an issue 500,000 Rs.1 ordinary shares whose current ex-dividend market price is Rs.1.5 per share. The company has just paid a dividend of 27 paisa per share, and dividends are expected to continue at this same level for some time. If the company has no debt capital, what is the cost of capital?

Cost of Retained Earnings and Cost of External Equity

Cost of equity = ke = dividend/market price per share = 0.27/1.5= 0.18 or 18% (growth rate of dividend = g = 0)Since there is no debt capital, cost of capital = 18%.

Example :Gorky Ltd. has got Rs. 5 lakhs of retained earnings and Rs. 5 lakhs of external equity through a fresh issue, in its capital structure. The equity investors expect a rate of return of 18%. The cost of issuing external equity is 3%. What is cost of retained earnings and the cost of external equity?

Cost of retained earnings: kr = ke = 18%

Cost of external equity = ke = kr /(1-f) = 0.18/(1-0.03) = 18.56%.

Cost of Retained Earnings and Cost of External Equity

P = ∑ I (1-t) / (1+kd)t + RV/ (1+kd)

n

t=1 to nWhere, kd = post-tax cost of debt

I = annual interest payment t = corporate tax rate RV = redemption value n = no. of years to redemption P = current market price of bondAn approximation formula , to save the trouble of doing an interpolation calculation, as given below can also be used.

Alternatively, kd can be estimated using the yield approximation method developed by Hawanini and Vora (1982). This is given by the following equation:

Where, P = Face value or per value NPD = Net proceed from sale or market value I,t, n = as above.

Cost of Debt

Example :Apeejay Limited has recently made an issue of non-convertible debentures for Rs.500 lakhs. The terms of the issue are as follows: each debenture has a face value of Rs.100 and carries a rate of interest of 15%. The interest is payable annually and the debenture is redeemable at a premium of 7% after 7 years. If Apeejay Limited realizes Rs.90 per debenture and the corporate tax rate is 50%, what is the cost of the debenture to the company?

kd = 15(1 – 0.5) + (107-90)/7 = 9.93 = 10.08%(107+90)/2 98.5

)

Cost of Debt

The cost of irredeemable preference share is equal to the cost of irredeemable bond or debenture .The cost of redeemable preference share (kp) is defined as that discount rate which equates the proceeds from preference capital issue to the payments associated with the same i.e., dividend payments and principal payments i.e.,

P = ∑ D / (1+kp)t + F/ (1+kp)n

t=1 to n

Where, kp = cost of preference capital D = annual preference dividend per share F = redemption value n = maturity period P = net amount realized per shareAn approximation formula , to save the trouble of doing an interpolation calculation, as given below can also be used.

kp = D + (F – P)/n(F + P)/2

Cost of Preference Capital

Example :

The terms of preference share issue made by Arjun Co. Ltd. are as follows: Each preference share has a face value of Rs.100 and carries a rate of dividend of Rs.15% payable annually. The share is redeemable after 10 years at par. If the net amount realized per share is Rs.105, what is the cost of preference share capital?

Given, D = 15, F = 100, P = 105, n =10

Cost of Preference Capital

Once the costs of a company’s individual sources of finance have been calculated, the overall weighted average cost of capital (WACC) can be determined. In order to calculate the WACC, the costs of the individual sources of finance are weighted according to their relative importance as a source of finance. WACC can be calculated either for the existing capital structure (average basis) or for additional incremental finance packages (marginal basis).

Weighted Average Cost of Capital (WACC)

WACC = Cost of equity*weight of equity + (1-tax rate) *Cost of Debt*weight of debt (considering only equity and debt)

Let a Company X & Co. has total capital structure C, E= value of equity share capital, R= value of retained-earning, P = value of preference capital, D = value of debenture, T=value of term loan, t= corporate tax rate, ke = cost of equity, kr =cost of retained

earning=ke, kp= cost of preference capital, kd = cost of debenture, ki = cost of term loan.

Then C= E+R+P+D+T

WACC = k e × E/C + k r × R/C + k p ×P/C +k d × D(1-t)/C +k t × T/C

= k e × We + k r × W r + k p W p + k d (1-t)Wd + k t × W t

= ∑k i W i for i = 1 to n, W i = (value of capital i)/ (value of total capital)

Market Value or Book Value Weights


DLPC Ltd is currently trying to work out its Weighted Average Cost of Capital (WACC). As a finance manager of the company find out that and show the necessary calculations .

In Rs.(0,000,000)

Fixed asset 545Current asset 135Current liabilities (210)

Total asset 470Ordinary Share capital(Rs.1per share) 90

10% preference shares(Rs.1.0 per share) (redeemable after 5 years)

40

Reserves 130

12% , 5 year redeemable debenture(15 crores) 150

Bank loans 60470

Balance sheet as on 31st March 2009


The current dividend, shortly to be paid, is 25 paisa per share. Dividends in future are expected to grow at a rate of 6% per year.

Corporate tax is currently 40%.The interest rate on bank borrowings is 11.55%.Stock market prices as on 31st march,2009

Ordinary shares: Rs. 5.6 per sharePreference shares: Rs.0.89 per share12% redeemable debenture: current market rate : Rs.9.5 per share

Cost of each sources of finance:1. Cost of equity:Using the Gordon model and ignoring issue cost

ke = Do(1+g)/Po + g = 0.25(1+0.06)/5.6 +0.06 = 10.73%2. Cost of retained earnings = kr = 10.73%3. Cost of preference shares: kp = D +(F-P)/n = 1+(1-0.89)/5 = 10.82% (F+P)/2 (1+0.89)/2


4. Cost of debenture :kd = I(1-t) +(RV-P)/n = 1.2(1- 0.4)+(10-9.5)/5 = 8.41%

(RV+P)/2 (10+9.5)/2

5. Cost of bank loan (after tax): ki = 11.55(1-0.4) = 6.93%

WACC (book value)= 10.73%*220/470 + 10.82*40/470 + 8.41%*150/470 + 6.93%*60/470 = 9.51% WACC (market value)= 10.73%*504/742.1 + 10.82%*35.6/742.1 + 8.41%*142.5/742.1 + 6.93%*60/742.1 = 9.98%

Source of Finance Book Value (Rs. Crores)

Market Value (Rs. Crores)

Equity 90+130 = 220 90*5.6 = 504Preference Shares 40 40*0.89 = 35.6Redeemable Debenture

150 15*9.5 = 142.5

Bank Loan 60 60Total 470 742.1


MC and AC of Capital

The marginal cost (MC) and average cost (AC) of capital

MC AC

Cost %

Gearing

Fundamentals of Capital Budgeting Decisions

Capital budgeting deals with the investment decisions that a company may undertake for the long-term profitability. This investment may involve purchase of stocks as well as new equipment, or even introduction of new products in the market.

Steps in CAPEX decisions:1. Identification of potential investment opportunities.

2. Assembling proposed investments.

3. Decision making.

4. Implementation.

5. Performance review.

• Stakeholders supply funds to a firm due to one simple reason. That reason, generally, is to receive a return on their precious resources.

• The management of the firm using the finance provided to invest mostly in capital assets generates the return.

• The objective of investment within a firm is to create value for its owners, the shareholders.

Value Creation and Corporate Investment

Cash flow tableCASH FLOWS

Cash Inflows Cash Outflows

Operational Flows Terminal Flows Initial Flows

Profit after tax plus Depreciation and otherNon-cash charges

Salvage value of fixed assets plus Salvage value of Net working capital

Outlays on Plant and machinery and other Fixed outlays on net working Capital.

Investment Appraisal Techniques: Non DCF and Chart

INVESTMENT APPRAISAL TECHNIQUES.

Decision AnalysisDecision Inputs

Cash flow projections and time value of money

Mainly DCF technique of evaluation

The fundamental question is a proposed course of action wealth creating ?

Decision

Yes No

Investment Appraisal Criteria

Non-DCF Criteria DCF Criteria

Payback Period Method (PBP)

Accounting Rate of Return (ARR)

Net Present Value Method (NPV)

Probability Index Method (P/I)

Internal Rate of Return Method (IRR)

Discounted Payback Period Method (DPBP)

Investment Appraisal Criteria

NPV (Net present Value)

Techniques: Decide on the discounting rate applicable for the project under review, keeping the risk exposure of the project into consideration. Estimate the future cash flows of the project over its useful life. Find out the present values of cash outflows and cash inflow. Compute NPV as follows. NPV=PV of cash inflows – PV of cash outflows.

Rules: •Accept projects with positive NPV. •Reject projects with negative NPV.•When comparison is made between two or more projects, the project with the highest positive NPV is undertaken.

Techniques: The profitability index is alternatively known as Desirability Factor (D/F) or Benefit Cost Ratio (BCR). P/I = PV of cash inflows / PV of cash outflows.

Rules:•Accept projects where P/I is greater than one.•Reject projects where P/I is less than one.

•When comparison is made between two or more projects, the project with the highest P/I is selected provided it is greater than one.

Profitability Index-P/I or Benefit Cost Ratio-BCR

Techniques: The Internal Rate of Return of a project is defined as that discount rate for which its NPV is equal to zero. In other words while applying the NPV technique, the discount rate is assumed and the NPV is assumed as zero and the corresponding discount rate is discovered (say by applying trial and error approach).

Rules: The project having the highest IRR is considered better and safer.

Internal Rate of Return - IRR

Technique:The payback period, defined as the expected number of years required to recover the original investment, was the first method used to evaluate capital budgeting projects. Rule: The shorter the payback period, the better.

Discounted Pay Back Period - DPBP

Technique: Under this system, the future cash flows are discounted prior to payback calculations. Rule: Same as PBP method

Pay Back Period - PBP

Accounting Rate of Return - ARR

Technique: ARR = Average Profit After Tax/ Average Book Value of the Investment

Rule: The ARR of a project is compared with the ARR of the firm as a whole or against some external yard-stick like the average rate of return for the industry as a whole.

Comparative Analysis of Investment Appraisal Techniques.NPV vs. IRR:

In certain situations, NPV and IRR may produce contradictory results. These different rankings may occur under the following circumstances.

Projects with unequal life.

If the projects are having different useful lives, it is perfectly possible that rankings may vary under NPV and IRR methods.

Mini Case

Let there be two projects X and Y of unequal life but equal initial investment. Project X’s life span is 1 year and project Y’s life span is 3 years. The initial cash outlay for both the projects is Rs 1,00,000. The cash proceeds for project X at the end of first year is Rs 1,50,000 and for project Y one-time cash generated at the end of third year is Rs 2,00,000. Assumed that the appropriate discount rate for both the projects is 12 %

Project Life

(year)

Initial outlay

(Rs.)

Cash proceeds in year 1

(Rs.)


(Rs.)


(Rs.)

Present value of cash

proceeds (discount rate

10%) (Rs.)

NPV

(Rs.)

IRR

X 1 100,000 150,000 133,930 33,930 50%

Y 3 100,000 200,000 142,356 42,356 26%

Projects with unequal life

Hence as per NPV rule project Y is better whereas, as per IRR rule project X is better .

Mutually exclusive proposals may differ on the basis of the pattern of cash flows generated although their initial investments are identical. This is known as the time disparity problem.

Mini CaseThe initial investment of both projects A and B is Rs 1,05,000. Useful lives in both cases = 4 years and appropriate discounting rate in both cases can be taken as 8%. The expected cash flows of the above projects for those 4 years are shown in the table below.

Project Initial investments

(Rs)

End of Year 1 (Rs)

End of Year 2 (Rs)

End of Year 3 (Rs)

End of Year 4 (Rs)

A 10,5000 60,000 45,000 30,000 15,000

B 10,5000 15,000 30,000 45,000 75,000

Table

Time disparity problem

NPV of project A= -- 105000 +(60000×0.9259) + (45000 × 0.8573) + (30000×0.7938) + (15,000×0.7350) = 23971.5

NPV of project B= --105000 +(15000×0.9259) + (30,000× 0.8573) + (45,000×0.7938) + (75,000×0.7350) = 25453.5

Hence project B is better as per NPV rule, but IRR of project A is higher than project B.

Time disparity problem

A and B are two mutually exclusive projects of life 1 year each involving different outlays. The effective rate of discount for both the projects can be taken as 10%. The relevant details of the projects are as follows.

A :- Initial Investment Rs 5,000 Cash Inflow Rs 6,250.B :- Initial Investment Rs 7,500 Cash Inflow Rs 9,150.

NPV of project A = -5000 + 6250/1.1= 681.82

NPV of project B = -7500 + 9150/1.1 = 818.20

IRR of project A = 6250/5000 – 1= 0.25 i.e. 25%

IRR of project B = 9150/7500 – 1 = 0.22 i.e. 22%

Hence as per NPV project B is better and whereas as per IRR project A is better.

This arises when initial investments in projects under consideration are different. In such situations the NPV and IRR may give different rankings.

Size disparity problem

It needs to be admitted that, IRR suffers from some inherent computational problems. It’s greatest demerit lies in the concept of reinvestment rate assumption, which is an implicit factor in IRR computation vis-à-vis decisions applying IRR method.

Mini caseThe life of both the projects A and B is two years and the appropriate rate of discount for both projects can be taken as 10%, and others are given in table.

Projects Initial Investment (Rs lakhs)

Cash Inflows (Rs lakhs)

NPV IRR

Year 1

A -20 40 14.78 100%

B -40 70 20.87 75%

As per NPV, B is better and as per IRR A is better

Drawback of IRR

Reasons for continued popularity of IRR1. Knowledge of required rate of return is not required.

In case of NPV calculations it is necessary to project future cash flows along with estimation of the required rate of return namely the cost of capital, which is applied as the discounting factor in NPV computation. It is needless to say that cost of capital estimation is a very complicated and tedious, exercise and none of the accepted techniques for the same are free from assumptions. Alternatively in IRR as computed is simply vetted against a pre specified cut off rate and the final decision is taken.

2. Lack of Knowledge

Some of the managers may not be fully aware or familiar with the inherent limitations of the IRR method and may be of the opinion that ranking can be accurately done with the aid of this method. 3. Psychological

Usually managers are comfortable in expressing financial data in the form of percentage.

Ranking Problem (IRR vis-à-vis NPV)

Table

Projects Cash Flows (Rs Lakhs) IRR (%) NPV applying1 year life Yr 0 Yr 1 15% discounting rate A (20) 40 100% 14.78 B (40) 70 75% 20.87

Computation of NPV applying different discount rates

Table

Discount Rate in % Project A Project B0 20 3020 13.33 18.3350 6.67 6.6775 2.86 0100 0 (5)125 (2.22) (8.89)

NPV vs. IRR graph

The MIRR is the rate of return ,which if used to compound the initial investment amount (i.e. the original cash outlay) produces the same terminal value as the project cash inflows.

Example The business development team of M/s A Limited has been working to find uses for a vacated factory premise. The two projects it has selected for further consideration by senior management both have a life of only three years, because the site will be flattened in three years when a new motorway would be constructed.

Modified Internal Rate of Return (MIRR)

On the basis of the IRR the business development team is leaning to words acceptance of project but it is aware that the key Senior Manager believes in MIRR and therefore feels the necessity to present the data calculated through the available techniques. The opportunity cost of capital is 10%.The following table shows cash flows and IRR of both the projects Figures in Rs.( ’000,000 ).

Time 0 1 2 3 IRR

Project A

-1 0.5

0.5

0.5 23.4%

Project B

-1 1.1

0.1

0.16

27.7%

You are required to complete the MIRR and NPV of both projects and show their ranking as per these Criteria.


Project IRR NPV MIRR

A 23.4% 0.24 18.3%

B 27.7% 0.20 17%

Decision B is better A is better A is better

MIRR calculations:

0.5(1+r)2 + 0.5(1+r)1 + 0.5(1+r)0 = (-1)(1+mirr)3 mirr = 18.3% for project A

1.1(1+r)2 + 0.1(1+r)1 + 0.16(1+r)0 = (-1)(1+mirr)3 mirr = 17% for project B

Therefore MIRR and NPV have given the same solution.


A company is planning to set up a project at a cost of Rs 3,00,00,000. It has to decide whether to locate the plant in Mumbai or Delhi (which is a backward district). Locating the plant in Delhi would mean a cash subsidy of Rs 15,00,000 from the central government. In addition to this, the taxable profit to the extent of 20 % would be exempted from taxes for a period of 10 years if the plant were to be located at Delhi.

The above project envisages a borrowing of Rs 2,00,00,000 in either case. The cost of borrowing will be 12 % for Mumbai and 10 % in case of Delhi. However, the revenue costs are likely to be higher in Delhi as compared to Mumbai. The borrowings have to be repaid in four equal annual instalments beginning from the end of the fourth year.

Case Study

With the help of information given in Table , please advise the management of the company as to where the project should be set up.

Note:

(a) A discount rate of 15 % can be assumed for computational purposes.

(b) Income tax rate applicable to the company is 50 % of their profits.

(c) Please apply the NPV criteria

Case Study

Year Profit / (Loss) before interest / depreciation and taxes (in Rs

lakhs).

Mumbai

Profit / (Loss) before interest / depreciation and taxes (in Rs lakhs).

Delhi

Discounting

Factors

applying a

rate of 15%

1 (6) (50) 0.87 2 34 (20) 0.76 3 54 10 0.66 4 75 20 0.57 5 110 50 0.50 6 140 100 0.43 7 150 150 0.38 8 250 200 0.33 9 350 225 0.28 10 450 350 0.25

Case Study

Solution: Mumbai: ( All figures are in Rs.’00,000).

Year EBDIT Depreciation

10% st. line

Interest

(12% of 200 lakhs or 2 crores)

PBT Tax

(50%)

PAT NCF

Net Cash Flow

=(PAT+Dep.—Cash out flow)

PV

Present value

15% discount factor

1 (6) (30) (24) (60) 0 (60) -100-30=-130 -113.12 34 (30) (24) (20) 0 (20) -20+30=10 7.63 54 (30) (24) 0 0 0 30 19.8

4 75 (30) (24) 21 0 21 -50+51=1 0.575 110 (30) (18) 62 1.5 60.5 -50+90.5=40.5 20.25

6 140 (30) (12) 98 49 49 -50+79=29 12.477 150 (30) (6) 114 57 57 -50+87=37 14.068 250 (30) 0 220 110 110 140 46.2

9 350 (30) 0 320 160 160 190 53.210 450 (30) 0 420 210 210 240 60

Total = 121.05

Case Study

Tax rule : Previous years losses will be compensated from future profit.

NPV for Mumbai = Rs.12105000. (positive), hence accept the project.For Delhi, For cash subsidy, Cash c/o at 0the year = (100-15) lakhs = Rs.

8,500,000 .Tax rate: for 20% exempted, therefore effective tax rate = 50% of 80% = 40%.By applying the similar methods, NPV for Delhi projects NPV = --Rs.17 lakhs.Hence it should be rejected.

Case Study

Example : ABC Limited is considering three financing plans. The key information is as follows. Total funds to be raised = Rs 2, 00,000 and plans of financing proportions are given in the Table below.

Pre tax cost of debt and cost of preference share can be taken as 8% each and the effective tax rate of the organization is 50%. It may also be noted that the company will be in a position to issue equity shares (face value Rs 10) at a premium of Rs 10 per share. The expected EBIT under all the financing plans can be taken as Rs 80,000.

Determine for each plan Earnings per equity share.Compute the EBIT range among the plans for indifference. Kindly indicate whether any of the plans dominate supported by adequate reasons.

Plans Equity Debt Preference Shares A 100% - - B 50% 50% - C 50% - 50%

Numerical Example

Plans A B C

100% equity 50% equity

50% debt

50% equity

50% preference shareNo. of equity shares 10,000 @Rs.10 5,000 @Rs.10 5,000 @Rs.10

Equity Rs.100,000 Rs.50,000 Rs.50,000Share Premium @Rs.10 Rs.100,000 Rs.50,000 Rs.50,000

Total equity Rs.200,000 Rs.100,000 Rs.100,000Preference Share @8% Rs.100,000Debt @8% Rs.100000

Total Capital Rs.200,000 Rs.200,000 Rs.200,000

EBIT 80,000 80,000 80,000

Less Interest @8% - -- 8000 -PBT 80,000 72,000 80,000Tax @50% 40,000 36,000 40,000PAT 40,000 36,000 40,000

Preference Dividend @8% - - -- 8,000

Earning Available to Equity Shareholders

40,000 36,000 32,000

EPS 4 7.2 6.4

b)EPS = (EBIT—Interest)(1—T) – Dp

No. of SharesLet EPS is equal for EBIT = xFor Plan A & B(x—0)0.5-- 0 = (x—8000)0.5 – 0 10000 5000EBIT = x = 16000 , indifferent of A & B.If x > 16000, plan B is better and if x < 16000, plan A is better.For Plan A & C(x—0)0.5-- 0 = (x—0)0.5 – 8000 10000 5000EBIT = x = 32000, indifferent of A & C.If x > 32000, plan C is better and if x < 32000, plan A is better.For Plan B & C(x—8000)0.5-- 0 = (x—0)0.5 – 8000 5000 5000

0.5x – 4000 = 0.5x – 8000For same amount of EBIT, EPS of B is more than C at every level of EPS.B would dominate than C due to tax implication (tax shelter).

Numerical Example

EBIT vs EPS graph

Finally, for upto EBIT = 16000, Option A will dominate (because of having more EPS) and beyond EBIT > 16000, Option B will predominate

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